<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We deal with an ordered weighted averaging operator (OWA operator) on the set of all fuzzy sets. Our starting point is OWA operator on any lattice introduced in Lizasoain, I.-Moreno,C.: OWA operators defined on complete lattices, Fuzzy Sets and Systems 224 (2013), 36-52; Ochoa, G.-Lizasoain, I.- -Paternain, D.-Bustince, H.-Pal, N. R.: Some properties of lattice OWA operators and their importance in image processing, in: Proc. of the 16th World Congress of the Internat. Systems Assoc.-IFSA ’15 and the 9th Conf. of the European Soc. for Fuzzy Logic and Technology-EUSFLAT ’15 (J. M. Alonso et al., eds.), Atlantis Press, Gijón, Spain, 2015, pp. 1261-1265. We focus on a particular case of lattice, namely that of all normal convex fuzzy sets in [0,1], and study algebraic properties and linearity of the proposed OWA operator. It is shown that the operator is an extension of standard OWA operator for real numbers and it possesses similar algebraic properties as standard one, however, it is neither homogeneous nor shift-invariant, i.e., it is not linear in contrast to the standard OWA operator.</p></abstract>

We deal with an ordered weighted averaging operator (OWA operator) on the set of all fuzzy sets. Our starting point is OWA operator on any lattice introduced in Lizasoain, I.-Moreno,C.: OWA operators defined on complete lattices, Fuzzy Sets and Systems 224 (2013), 36-52; Ochoa, G.-Lizasoain, I.- -Paternain, D.-Bustince, H.-Pal, N. R.: Some properties of lattice OWA operators and their importance in image processing, in: Proc. of the 16th World Congress of the Internat. Systems Assoc.-IFSA ’15 and the 9th Conf. of the European Soc. for Fuzzy Logic and Technology-EUSFLAT ’15 (J. M. Alonso et al., eds.), Atlantis Press, Gijón, Spain, 2015, pp. 1261-1265. We focus on a particular case of lattice, namely that of all normal convex fuzzy sets in [0,1], and study algebraic properties and linearity of the proposed OWA operator. It is shown that the operator is an extension of standard OWA operator for real numbers and it possesses similar algebraic properties as standard one, however, it is neither homogeneous nor shift-invariant, i.e., it is not linear in contrast to the standard OWA operator.

On Algebraic Properties and Linearity of Owa Operators for Fuzzy Sets

Institute of Information Engineering Automation and Mathematics Faculty of Chemical an Food Technology Slovak University of Technology in Bratislava Radlinského 9 SK–812-37 Bratislava,

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"On Algebraic Properties and Linearity of Owa Operators for Fuzzy Sets"}

We deal with an ordered weighted averaging operator (OWA operator) on the set of all fuzzy sets. Our starting point is OWA operator on any lattice introduced...

On Algebraic Properties and Linearity of Owa Operators for Fuzzy Sets

Published Online: Jan 20, 2017

Page range: 137 - 149

Received: Jul 15, 2016

DOI: https://doi.org/10.1515/tmmp-2016-0026

Keywords
OWA operator, type-2 fuzzy set, fuzzy set, fuzzy truth value, aggregation, distributive weighting vector

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

On Algebraic Properties and Linearity of Owa Operators for Fuzzy Sets

Published Online: Jan 20, 2017

Page range: 137 - 149

Received: Jul 15, 2016

DOI: https://doi.org/10.1515/tmmp-2016-0026

KeywordsOWA operator, type-2 fuzzy set, fuzzy set, fuzzy truth value, aggregation, distributive weighting vector

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
OWA operator, type-2 fuzzy set, fuzzy set, fuzzy truth value, aggregation, distributive weighting vector